After a very long and boring playthrough, I have calculated the odds of drawing each weapon from the mystery box. This is based off of 200 draws in a row from the mystery box without it moving from it's original location. I won't be doing any other tests since each box spot has different odds as well as the number of times it's moved.
Der Riese
Appearing in order of most to least common
Monkey Bombs: 12.5%
Type 100: 8%
WunderWaffe DG-2: 7.5%
FG-42: 7%
MP40: 6.5%
BAR: 6.5%
Trench Gun: 5.5%
PPSH-41: 4.5%
M1 Garand: 4%
Molotov: 4%
Kar98K: 4%
Thompson: 3.5%
PTRS-41: 3.5%
Flamethrower: 3.5%
M1A1 Carbine: 3%
STG-44: 3%
MG42: 2.5%
Browning: 2.5%
Panzershrek: 2%
Double Barrel Shotgun: 1.5%
Raygun: 0%
Yep, out of 200 draws in a row, the raygun didn't even appear once.